Narrow-Band Correction of the Residual Amplitude Modulation in FM

Frequency Measurement of an Ar+ Laser Stabilized on Narrow Lines of Molecular Iodine at 501.7 nm F. du Burck, C. Daussy, A. Amy-Klein, A. N. Goncharov†, O. Lopez, C. Chardonnet, J.-P. Wallerand* Laboratoire de Physique des Lasers, UMR 7538 CNRS, Université Paris 13 99 av. J.-B. Clément, 93430 Villetaneuse, France † permanent address: Institute of Laser Physics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia *permanent address: BNM-INM/CNAM 292 rue Saint Martin, 75003 Paris, France Abstract–A spectrometer for ultra high-resolution spectroscopy of molecular iodine at wave length 501.7 nm, near the dissociation limit is described. Line shapes about 30 kHz wide (HWHM) were obtained using saturation spectroscopy in a pumped cell. The frequency of an Ar+ laser was locked to a hyperfine component of the R(26)62-0 transition and the first absolute frequency measurement of this line is reported. Index terms–Iodine spectroscopy, FM spectroscopy, residual amplitude modulation, optical frequency measurement 1 I. INTRODUCTION Molecular iodine shows a rich absorption spectrum from 900 nm to 500 nm (the dissociation limit of the molecule), consisting of about 100 000 rovibrational transitions between the fundamental 1 3 electronic state X ( Σ0+g) and the excited state B ( Π0+u). Each of these shows a hyperfine structure. The natural width of these components is determined by their radiative width and by predissociation effects. These latter result from the gyroscopic and hyperfine couplings between the 3 1 excited state Π0+u and the dissociative state Π1u [1]. Both radiative and predissociative widths decrease near the dissociation limit. In particular, direct lifetime measurements by fluorescence decay have shown that the hyperfine components of the R(26)62-0 transition, accessible with an Ar+ laser at 501.7 nm, should have a natural linewidth around 10 kHz [2]. Such narrow lines are of particular interest for the realization of highly stable optical frequency standards. Moreover, a better accuracy is expected, because most of the systematic errors and some experimental errors like the effect of line distortion are proportional to the linewidth. However, in a recent study of the transitions in the region 523 nm - 498 nm, the narrowest natural linewidth was estimated to be 43 kHz [3], using experimental data obtained in a sealed cell. In a previous work, in which hyperfine components of transition R(26)62-0 were detected on a supersonic beam, we obtained a linewidth of 30 kHz [4]. We present here lineshapes with a similar width obtained in saturation spectroscopy in a pumped cell. We locked the laser frequency onto these narrow lines and carried out the first absolute frequency measurement of this transition. II. THE SPECTROMETER + + Fig. 1 depicts the Ar /I2 stabilization set-up. The single mode Ar laser is prestabilized on a Fabry- Perot resonator mode (finesse 660, free spectral range 1 GHz) by a classic Pound-Drever technique, in order to reduce its frequency jitter. For the long-term stabilization, the prestabilized laser is locked to a hyperfine component of the R(26)62-0 transition of iodine at 501.7 nm detected with 2 the saturation spectroscopy technique in a 50 cm long sealed cell (cell 1) (switches in position 1 in Fig. 1). The iodine pressure in the cell, of about 3.3 Pa (25 mTorr), is controlled by the thermostabilization of the cell cold finger. Probe and pump beam frequencies are shifted by 250 MHz and 80 MHz respectively by the acousto-optic modulators (AOM) AOM1 and AOM2. The error signal for the long-term stabilization of the laser is obtained by the modulation transfer technique: the pump beam is frequency modulated at 125 kHz by AOM2 and the first harmonic of the saturated absorption signal is detected with the probe beam. The correction signal for frequency stabilization is applied to a piezoceramic transducer that controls the length of the Fabry-Perot resonator. In the long-term laser stabilization, the correction bandwidth is limited by the signal-to-noise ratio (SNR) of the detected signal. We have developed an original narrow-band controller based on an adaptive noise cancelling technique for the stabilization of the beam power in the vicinity of the modulation frequency [5]. The probe beam intensity at the input of the cell is monitored by photodiode PD3 to generate the error signal applied to the narrow-band controller. It drives the RF input power of AOM1 which is used as the actuator. The closed loop system is equivalent to a notch filter tuned to the modulation frequency. The noise rejection efficiency in a narrow-band centred at 125 kHz is illustrated in Fig. 2. It shows the spectral density of the signal of photodiode PD2 located at the output of the cell. A notch in the intensity noise near 125 kHz is clearly seen. The noise is rejected by 27 dB, only 9 dB above the electronic noise level. Iodine spectroscopy is performed in a low-pressure cell (cell 2 in Fig. 1) in order to record narrow lines. Probe and pump beam frequencies are shifted by 250 MHz and 80 MHz respectively by AOM3 and AOM4. Then, the beams cross a telescope with a pinhole to limit the transit effect in the I2 cell and to improve the wavefront quality. The beam diameter in the cell is 6 mm. The hyperfine transition is detected using saturated absorption spectroscopy using the technique of frequency modulation (FM) spectroscopy [6, 7]. The modulation frequency applied to the probe 3 beam is 2.5 MHz, a frequency for which the technical noise of the laser is negligible. However, it is well-known that a persistent problem of FM spectroscopy is the sensitivity of the detected signal to the residual amplitude modulation (RAM) generated by the frequency or phase modulator. The detection of this RAM gives a non-zero baseline and the technical noise of the laser is transferred at the detection frequency [8]. The RAM also generates a distortion of the detected line shape [9]. We use a narrow-band controller to reject the RAM of the probe beam at 2.5 MHz [10]. The error signal is obtained from a photodiode (PD4) monitoring the probe beam intensity at the input of the cell and an AOM (AOM3) driven by the cancelling signal controls the beam intensity. In our set- up, the probe beam may be phase-modulated by an electro-optic modulator (EOM), as is usual in FM spectroscopy. But, in order to simplify the scheme, the modulation may also be applied directly to AOM3 used for the intensity stabilization as shown in Fig. 1. The beam is then frequency- modulated. In this case, although the AOM introduces a spatial modulation of the beam, a 40-50 dB rejection of the 2.5 MHz RAM component may be achieved by a careful alignment of both photodiodes PD4 and PD5 on the beams [10]. Another feature of our set-up is the low-pressure iodine cell (cell 2) for the detection of narrow lines. It is 4 m long and its diameter is 15 cm. This cell may be pumped during the experiment to minimize buffer gas and impurity effects. Indeed, the width of the studied transitions at 501.7 nm is known to be very sensitive to the impurities present in the cell [11]. An iodine crystal is formed in the cell before the experiment and the iodine pressure, in the range 0.07 Pa – 0.7 Pa (0.5 mTorr – 5 mTorr), is controlled by thermostabilization of a cold finger. This cell was used in previous work for the study of transitions between hyperfine levels of the ground rovibrational states of iodine. We obtained linewidths of 2.6 kHz in stimulated Raman spectroscopy and 2.1 kHz in resonant Rayleigh spectroscopy [12, 13]. We conclude that the upper limit of impurity pressure in the cell is less than 0.04 Pa (0.3 mTorr) and that the cell itself does not limit the resolution of our experiment. 4 II. THE NARROW DETECTED LINES One of the narrowest line detected at 501.7 nm is shown in Fig. 3. It corresponds to the hyperfine component a7 of transition R(26)62-0. The probe beam was frequency-modulated at 2.5 MHz by the AOM. The pressure in cell 2 was about 0.066 Pa (0.5 mTorr). The solid curve results from the fit of experimental data with the imaginary part of a Lorentzian with a half-width at half-maximum (HWHM) of 32 kHz. The laser frequency locked to this hyperfine component was measured using a femtosecond optical frequency comb. In order to increase the signal to noise ratio (SNR) of the error signal, we worked with a pressure of 0.33 Pa (2.5 mTorr) in the cell. For this pressure, the linewidth was HWHM = 45 kHz. IV. THE FREQUENCY MEASUREMENT SET-UP For the frequency measurements at 501.7 nm, the laser frequency was locked to the hyperfine component a7 of transition R(26)62-0 detected in the 4-m long low-pressure cell (cell 2) instead of the sealed cell (switches in position 2 in Fig. 1). An additional 200 Hz amplitude modulation of the pump beam was introduced and a second lock-in amplifier was used in order to eliminate the residual offset of the error signal due to the Doppler background. A small amount of Ar+ laser power is directed along a polarization maintaining single mode fibre to the room where the femtosecond comb generator set-up is located. The set-up for frequency measurements at 501.7 nm is essentially similar to the one used in a previous work for absolute frequency measurement at 514.6 nm [14].

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